Application of Reliability Theory to Insurance

1. There is a general rule applicable to all insurance and reinsurance fields according to which the level of the so-called technical minimum premium should be fixed such that a certain stability criterion is satisfied for the portfolio under consideration. The two bestknown such criteria are (i) the probability that there is a technical loss in any of the future years should be less than a given percentage (ii) the probability that the company gets "ruined” i.e. initial reserves plus accumulated premiums minus accumulated claims becomes negative at any time of a given period in the future should be less than a tolerated percentage. Confining ourselves to criterion (i) in the present paper we may then say that the problem of calculating technical minimum premiums is broadly spoken equivalent with the problem of estimating loss probabilities. Since an exact calculation of such probabilities is only possible for a few very simple and therefore mostly unrealistic risk models and since e.g. Esscher's method is not always very easy to apply in practice it might be worthwhile to describe in the following an alternative approach using results and techniques from Reliability Theory in order to establish bounds for unknown loss probabilities. It would have been impossible for me to write this paper without having had the opportunity of numerous discussions with the Reliability experts R. Barlow and F. Proschan while I was at Stanford University. In particular I was told the elegant proof of theorem 3 given below by R. Barlow recentl

Estimation of the number of excess claims by means of the credibility theory

The purpose of this paper is to describe a possible application on the rating of excess of loss covers of Mr. Bühlmann's work on Experience Rating and Credibility). One of the most important problems in connection with the rating of such treaties consists in estimating the number of excess claims and the average excess claim amount. Especially with cases where claims data are scarce there is a temptation to estimate these two quantities by means of the credibility theory. This approach leads, on the one hand, to a relatively complicated formula when considering the average excess claim amount, and, on the other, to a rather simple one for the credibility factor of the number of excess claim

Application of higher harmonic blade feathering on the OH-6A helicopter for vibration reduction

The design, implementation, and flight test results of higher harmonic blade feathering for vibration reduction on the OH-6A helicopter are described. The higher harmonic control (HHC) system superimposes fourth harmonic inputs upon the stationary swashplate. These inputs are transformed into 3P, 4P and 5P blade feathering angles. This results in modified blade loads and reduced fuselage vibrations. The primary elements of this adaptive vibration suppression system are: (1) acceleration transducers sensing the vibratory response of the fuselage; (2) a higher harmonic blade pitch actuator system; (3) a flightworthy microcomputer, incorporating the algorithm for reducing vibrations, and (4) a signal conditioning system, interfacing between the sensors, the microcomputer and the HHC actuators. The program consisted of three distinct phases. First, the HHC system was designed and implemented on the MDHC OH-6A helicopter. Then, the open loop, or manual controlled, flight tests were performed, and finally, the closed loop adaptive control system was tested. In 1983, one portion of the closed loop testing was performed, and in 1984, additional closed loop tests were conducted with improved software. With the HHC system engaged, the 4P pilot seat vibration levels were significantly lower than the baseline ON-6A levels. Moreover, the system did not adversely affect blade loads or helicopter performance. In conclusion, this successful proof of concept project demonstrated HHC to be a viable vibration suppression mechanism